About this question
Hard · Probability & Statistics · Quant Trader interview question · probability, graph-theory, erdos-renyi, threshold
Consider an Erdős–Rényi random graph $G(n, p)$ where $n$ represents the number of vertices and $p$ represents the probability of an edge existing between any two vertices. You are tasked with determining the sharp threshold for $p$ at which the graph becomes almost surely connected as $n$ approaches infinity. This means you need to find the smallest value of $p$ such that the probability of the graph being connected approaches 1 as $n$ grows large. What is the sharp threshold for $p$ at which th